Expectation has been drained from Liverpool's continental campaign. The memory of their mesmerising opening victory over Monaco in Group A was obliterated in Greece last night, lost in the trauma of a defeat far more emphatic than the scoreline suggests. Rafael Benítez regularly pleads for time; on this evidence he will need it.

This was a painful reality check in Piraeus. Olympiakos dismissed Liverpool with ease, the visitors' lacklustre display drowned amid a joyous cacophony at the final whistle. Liverpool were bullied in the air, embarrassed on the turf and appeared to lack the strong-arm spirit to revive, their zip still elusive when necessity demanded a more urgent approach late on.

This was Liverpool's first defeat on Greek soil but, more significantly, it provided Benítez with another insight into the onerous task he has undertaken. Only Manchester United, twice, and Juventus have prevailed in these parts at Olympiakos's expense in 23 games among the elite. The Spaniard's former club, Valencia, might have flourished here; Liverpool floundered.

"We lost possession too easily, particularly in the first half," said Benítez. "We never kept the ball." That is becoming a troublingly familiar trait away, where Liverpool's form has been too insipid for comfort to date, the slick passes at Anfield often lost in an incoherent mishmash. There was to be no exception here. The home goalkeeper Antonios Nikopolidis barely had a save to make, with Liverpool utterly unable to rouse themselves even after Anastasios Pantos had been dismissed for two bookings.

Instead, Liverpool players bickered among themselves as they departed the scene in the raucous din, frustration nagging at them as acrid flare smoke rolled across the arena. Ieroklis Stoltidis had headed against the crossbar and Stylianos Venetidis, meandering through a shambolic offside trap, had dragged a shot wastefully wide even in the six minutes Liverpool held a numerical advantage. That told its own story of the Premiership side's inadequacies.

Even Xabi Alonso, normally imperious, was made to look mediocre in the home side's onslaught, Liverpool gasping for breath amid rampant early Greek attacks. Only when the home players opted to crumple to the turf under the vaguest hint of a challenge - something they did shamelessly and regularly - did Liverpool find any respite, though it was through a set piece that Olympiakos took their goal.

It was Rivaldo who regularly prompted the panic. The 32-year-old wears No5 these days and the consensus is that he is half the player he was when, as Brazil's No10, he helped inspire them to the World Cup two years ago. Yet from set plays his class still shines through. There was a reverse flick at the kick-off to set the tone, a blistering volley from distance which burst beyond Jerzy Dudek but wide of a post, before he ambled, bandy-legged, up for a succession of free-kicks near Liverpool's penalty area.

From one - Stephen Warnock having apparently obstructed Dimitrios Mavrogenidis - Rivaldo's centre flicked off Milan Baros, barely 10 yards from the Brazilian, to veer awkwardly into the area. Dudek and his defenders were too static to repel the threat. Sami Hyypia was flummoxed by the deflection and Stoltidis, leaping on the penalty spot, flicked the loose ball home. Benítez, who saw his side concede twice from set pieces at United last week, was apoplectic on the bench.

His mood must have been black already. Stoltidis, freed by Ioannis Okkas early on, forced Dudek to touch a shot on to his near post. By half-time the Brazilian Giovanni and Pantelis Kafes should both have converted close-range headers as Liverpool wilted. The nearest they came to a riposte was Baros's pass which slipped the substitute Harry Kewell in on goal, only for a linesman to choke the Australian's attempt before the goalkeeper could.

Improvement will be needed against Benítez's compatriots Deportivo La Coruña in back-to-back fixtures to come, and the quicker Liverpool can put this ignominy behind them the better. Olympiakos's delight was unconfined; after their success at Euro 2004, Greek football has never enjoyed days as heady as these.